The Asiatic Jasmine is widely used in mild areas. The Asiatic Jasmine ground cover is a twining rambler with long woody stems. The Asiatic Jasmine grows best in fairly rich soil and requires regular watering. Fragrant blossoms cover the Asiatic Jasmine.Call today and speak with our operators, waiting to take your order of Asiatic Jasmine! The Asiatic Jasmine has oval, deep-green leaves with small, sweetly fragrant, star-like flowers that appear from early Spring through Summer.